On the Space of Orthonormal Wavelets: Additional Constraints to Ensure Two Vanishing Moments

Sba Controle & Automação

Galvão

Rodrigues

2009

Self Cite

This paper presents a multivariable extension to a recently proposed wavelet-based technique for fault detection. In the original formulation, the Discrete Wavelet Transform is used to carry out dynamic consistency checks between pairs of signals within frequency subbands. For this purpose, moving average models with an integrative term are employed to reproduce the dynamics of the system in each subband under consideration. The present work introduces a new architecture allowing the use of subband models with more general multivariable structures. More specifically, a multivariable ARX (autoregressive with exogenous input) structure is adopted for each subband model. The proposed technique is illustrated in a case study involving a nonlinear simulation model for an aircraft with a sensor fault. The results show that the multivariable approach outperforms the original formulation in terms of residue amplification following the fault onset.

Section: Discussionmentioning

confidence: 99%

A wavelet-based multivariable approach for fault detection in dynamic systems

Sba Controle & Automação

Galvão

Rodrigues

2009

Self Cite

“…However, after obtaining the constraints that ensure at least two vanishing moments, in [9], other papers have presented the use of that formulation and this restriction to various applications, some examples are, [3,8,6]. The restriction achieved in this paper ensures at least three vanishing moments and was already applied to fault detection in [12], presenting promising results.…”

Section: Introductionmentioning

confidence: 93%

“…However, initially there were no constraints to ensure a number of vanishing moments greater than one. An extension of this formulation introducing restrictions to ensure two vanishing moments was done by [9]. In [13] the constraints to ensure at least three vanishing moments were presented.…”

Section: Transient Detection In a Signalmentioning

confidence: 99%

“…Additional constraints to ensure at least two vanishing moments were obtained by [9]. This article is an extension of [13] presenting an improvement to the formulation of [11].…”

Section: Introductionmentioning

confidence: 99%

“…This article is an extension of [13] presenting an improvement to the formulation of [11]. In order to ensure a third vanishing moment for wavelet filter banks, additional constraints are presented to the work of [9] and [11]. An application of the formulation with three vanishing moments for transient detection is presented in this paper.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Additional constraints to ensure three vanishing moments for orthonormal wavelet filter banks and transient detection

Uzinski

Tend. Mat. Apl. Comput.

Villareal

et al. 2015

Self Cite

A Dynamic-State Feedback Approach Employing a New State-Space Description for the Fast Wavelet Transform with Multiple Decomposition Levels

Uzinski

J Control Autom Electr Syst

Galvão

et al. 2017

This research paper proposes a wavelet-based dynamic-state feedback control strategy in the discrete time domain. In this proposal, the state feedback employs a statespace description for the fast wavelet transform, which is also developed in this article. The feedback gains are obtained through a linear quadratic regulator formulation, with cost weights adjusted according to suitable performance metrics. This proposal brings forward efficient results, as well as more robust systems to external perturbations and sensor noises.